Course Information


Course Information
Course Title Code Semester L+U Hour Credits ECTS
CALCULUS II MTH0142 2. Semester 4 + 0 4.0 6.0

Prerequisites None

Language of Instruction English
Course Level Bachelor's Degree
Course Type Compulsory
Mode of delivery
Course Coordinator
Instructors
Assistants
Goals This lecture deals with definite integral and its applications, sequence and series and their convergence, Taylor series, definition of multivariable function and partial definiton, evaluation of double and triple integration and their applications.
Course Content Evaluation and applications of the definite integral, improper integral, Definition of the sequence and the series, power series, multivariable functions and their limit, continuity, partial derivatives, double and triple integrals, evaluation of triple integrals in cylindric and spherical coordinates and their applications
Learning Outcomes 1) Learns the notion of definite integral and its applications.
2) Investigates convergence behaviour of series and Taylor Series.
3) Finds the local and absolute extremums of functions with several variables
4) Finds the exact differential of functions of several variables and makes an approximate calculations using this exact differential
5) Learns the meaning of partial derivatives in a geometric way.
6) Calculates double integrals and by using these integrals solve the problems of area, volume problems

Weekly Topics (Content)
Week Topics Teaching and Learning Methods and Techniques Study Materials
1. Week Riemann's sum, the definite integral, fundamental theorem of calculus Lecture; Question Answer; Problem Solving; Discussion
Colloquium
Problem Based Learning 		Homework
2. Week Applications of definite integrals, area calculation, Volume calculation (Cross method) Lecture; Question Answer; Problem Solving; Discussion
Colloquium
Problem Based Learning 		Homework
3. Week Volume calculation (disc and shell methods), the curve length of the calculation Lecture; Question Answer; Problem Solving; Discussion
Colloquium
Problem Based Learning 		Homework
4. Week Parametric equations and lengths of the curves, areas of surfaces of revolution Lecture; Question Answer; Problem Solving; Discussion
Colloquium
Problem Based Learning 		Homework
5. Week Generalized integrals and convergence tests Lecture; Question Answer; Problem Solving; Discussion
Colloquium
Problem Based Learning 		Homework
6. Week Polar coordinates Lecture; Question Answer; Problem Solving; Discussion
Colloquium
Problem Based Learning 		Homework
7. Week Curve sketching in polar coordinates Lecture; Question Answer; Problem Solving; Discussion
Colloquium
Problem Based Learning 		Homework
8. Week Arrays, arrays limit Lecture; Question Answer; Problem Solving; Discussion
Colloquium
Problem Based Learning 		Homework
9. Week Series, convergence tests for series with positive terms Lecture; Question Answer; Problem Solving; Discussion
Colloquium
Problem Based Learning 		Homework
10. Week Alternating series, absolute and conditional convergence Lecture; Question Answer; Problem Solving; Discussion
Colloquium
Problem Based Learning 		Homework
11. Week Power series, Taylor series Lecture; Question Answer; Problem Solving; Discussion
Colloquium
Problem Based Learning 		Homework
12. Week Limits and continuity of functions of several variables Lecture; Question Answer; Problem Solving; Discussion
Colloquium
Problem Based Learning 		Homework
13. Week Partial derivatives, chain rule Lecture; Question Answer; Problem Solving; Discussion
Colloquium
Problem Based Learning 		Homework
14. Week Area transformations and double integrals Lecture; Question Answer; Problem Solving; Discussion
Colloquium
Problem Based Learning 		Homework

Sources Used in This Course
Recommended Sources
Calculus with Analytic Geometry, C.H. Edwards, D.A. Penney, Prentice Hall, 1997.
Calculus, James Stewart, Thomson 2003.
Thomas’Calculus, George B. Thomas, Pearson 2005.

ECTS credits and course workload
Event Quantity Duration (Hour) Total Workload (Hour)
Course Duration (Total weeks*Hours per week) 14 4
Work Hour outside Classroom (Preparation, strengthening) 14 2
Midterm Exam 2 2
Time to prepare for Midterm Exam 2 20
Final Exam 1 2
Time to prepare for Final Exam 1 37
Total Workload
Total Workload / 30 (s)
ECTS Credit of the Course
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Course Information
  • Course Information
  • Weekly Topics (Content)
  • Sources Used in This Course
  • ECTS credits and course workload